4. Nonmechanistic models

aerobically and anaerobically. Ethanol can be used as a carbon source only aerobically. Then, different sets of linear algebraic equations can be derived concerning

The respiratory quotient (RQ ) is often used as an indicator of fermentative processes. When RQ is close to one, there is no fermentative metabolism, whereas if

<sup>¼</sup> >1, fermentative metabolism

The mechanistic characteristics of an unstructured, unsegregated kinetic model contribute to the knowledge of the complex metabolism of S. cerevisiae. Despite giving relevant information of simple metabolic processes with multiple

reactions, UKMs cannot give information about complete intracellular oxidative metabolism. An example of the application of these models is explained in

There are several classifications of mechanistic and statistical models of cell population for bioprocess applications. Two terms are essential for mathematical description of cell populations: segregated and structured models. A structured model is related to cell material description using multiple chemical components. A segregate model is related to the description of individual cells in a heterogeneous population. Additionally, it is possible to combine a structured approach with a segregated approach. Structured kinetic models are introduced in this section.

Structured kinetic models (SKMs) describe changes in cell population. The liq-

Morphologically structured models consider the kinetics of nutrient consumption and product formation. These models consider different cell types as living species in terms of the role that they play in the overall reaction. Chemically structured models consider the effects of chemical species in fermentation kinetics; all viable cells are functionally similar, and all the fermentation rates and transport phenomena parameters are accounted for. Genetically structured models assume molecular mechanism knowledge. The model includes the rate of expression of an operator-regulated gene and kinetic equations for the transcription, translation, and folding processes. Metabolically structured models provide a better understanding of process regulation mechanisms such as feedback regulation. This model is based on the main metabolic pathways and in most cases is included in MFA. In the

uid phase (abiotic phase) usually contains nutrients for cell growth and some extracellular metabolites. The microorganisms suspended in the liquid phase behave as multicomponent systems. SKMs consider the internal structure of cells (e.g. mitochondria), and the description of cell growth and its metabolism is used to assume a more accurate growth rate. The information used is a starting point to generate schemes that represent more accurately the growth of microorganisms and their cellular components. The complexity of the information variables and parameters increases in SKMs with the mathematical representation of cellular growth. SKMs are generally classified into morphologically structured models, chemically structured models, genetically structured models, and metabolically structured

≈1, non fermentative metabolism

(11)

carbon, oxygen, and hydrogen balance.

Current Topics in Biochemical Engineering

subsequent sections.

models [20].

16

3. Structured growth kinetics

3.1 Simple structured kinetic models

RQ is above one, the fermentative metabolism occurs.

  RQ <sup>¼</sup> rCO<sup>2</sup> rO<sup>2</sup> 

> The structured and unstructured kinetic models in the previous sections describe, with a high degree of accuracy, the dynamic behavior of microbial growth in bioreactors. These models, associated with material and energy balances, also help to understand the phenomena associated with microbial metabolism, giving clues to the process design and control.

> Black box models (BBMs) usually fall into two main categories: statistical models (SMs) and artificial intelligence tools (AITs). SMs use experimental design, response surface analysis, and exploratory data analysis, whereas AITs consider tools such as data mining, artificial networks, and fuzzy logic [22]. Also, several methodologies to combine mechanistic approaches with nonmechanistic modeling strategies have been developed. The hybrid models, which are known as gray box models (GBMs), inherit the advantages of BBMs such as data analysis and can achieve semi-mechanistic description to each metabolic phenomenon. GBMs offer greater estimation accuracy, calibration ease, better extrapolation properties, and more detailed information on the phenomenology of the system [23]. The advantages of GBMs in the application of bioreactor modeling are direct control and optimization. In this section, we will describe some of these nonmechanistic modeling tools and some of their applications, such as the design of soft sensors.
